Resource Allocation

Consider a network where each source r is identified by an origin and a destination between which the user of source r is transferring data. In addition, we suppose that each source r uses a fixed route between its origin and destination, and that the route is specified by a sequence of links. Thus, the index r can be used to denote both the source and the route used by the source. Let x _r be the rate (bits/sec. or bps) at which source r is allowed to transmit data. Each link l in the network has a capacity c _l bps. Given the capacity constraints on the links, the resource allocation problem is one of assigning rates {x _r } to the users in a fair manner. To illustrate the difficulties in destination, a fair resource allocation, we consider the following simple example of a network with three links and two sources.